Cortical neuron classes and recursive curvature collapse: a neurobiological model of conscious dynamics

Abstract

Understanding how conscious cognition remains stable under uncertainty, conflict, and perturbation requires a framework that links neural dynamics to the geometry of evolving representational states. Here we develop Recursive Informational Curvature (RIC), a neurogeometric framework in which conscious access is modeled as a stability regime of trajectories on a stratified informational manifold. In this framework, recursive gain, symbolic entropy dispersion, and loop-level timing coherence jointly determine whether neural activity remains within closure-supporting regimes or approaches collapse. We formalize this balance through an effective curvature index, \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{K}(t)$$\end{document}, defined relative to a declared critical boundary \documentclass12pt{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{K}}_{ ext{c} ext{r} ext{i} ext{t}}$$\end{document}, and through circulation-based timing statistics that quantify phase-organized loop stability. The theory integrates three coupled geometric layers: a Fisher layer for precision-weighted discriminability, a Finsler layer for direction-dependent transition cost, and a Hermitian layer for phase-coded recursive coordination. We further propose mechanistic hypotheses linking identifiable cortical neuronal classes, including mirror circuits, von Economo neuron-rich salience territories, TPJ mentalizing ensembles, and prefrontal phase-modulating hubs, to class-specific curvature control. To connect the framework to data, we specify measurement-facing estimators for gain, symbolic entropy structure, loop instability, and effective curvature, and we provide a reduced EEG-based empirical analysis showing that a geometry-sensitive neural state-space proxy is related to moral judgment bias, while broader socially mediated outcomes are not captured by this reduced measure alone. RIC therefore offers a formal and operational framework for studying stability, collapse, and recovery in conscious dynamics across theoretical, empirical, and translational settings.